The coordinates a(0, 0), b(0, 4), c(3, 4) and d(3, 0) are graphed and connected together. what 3-dimensional shape will be created when this shape is rotated about the y-axis? provide an explanation and proof for your answer to receive full credit. (10 points)

cylinder

Step-by-step explanation:

The coordinates A(0, 0), B(0, 4), C(3, 4) and D(3, 0) are graphed and connected together (see attached diagram). Points A, B, C and D form rectangle with side AD on the x-axis and side AB on the y-axis.

When rectangle ABCD will be rotated about the y-axis, then the created shape will be the cylinder with circle base of the radius AD and height of the length AB (see attached diagram).

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).